What is the volume formula for a right circular cylinder?

The volume formula for a right circular cylinder is derived from the geometric understanding of the shape. A right circular cylinder consists of two parallel circular bases and a height extending between them. The volume of a cylinder can be calculated by finding the area of one of its circular bases and then multiplying this area by the height of the cylinder.

To calculate the area of the base, which is a circle, the formula used is (πr^2), where (r) is the radius of the circular base. Once the area of the base is determined, multiplying that area by the height (h) of the cylinder gives the total volume. Therefore, the formula for the volume (V) of the cylinder becomes:

[

V = \text{Area of the base} \times \text{Height} = πr^2 \times h

]

Thus, the formula (V = πr^2h) accurately represents the volume of a right circular cylinder, making it the correct choice. The other options presented do not reflect the standard derivation for calculating the volume of a right circular cylinder.